— For an Estimation Based Multiple Model Switched Adaptive Control (EMMSAC) algorithm controlling a MIMO minimal LTI plant, lp, 1 ≤ p ≤ ∞ bounds on the gain from the input and output disturbances to the internal signals are obtained which are invariant to the number of models in the plant model set. For a compact uncertainty set it is shown that a realisable EMMSAC algorithm achieves robust stability for any plant within the uncertainty set.